Question

Write plausible molecular orbital diagrams for the following heteronuclear diatomic species: (a) \(\mathrm{NO} ;\) (b) \(\mathrm{NO}^{+}\) (c) \(\mathrm{CO} ;\) (d) \(\mathrm{CN} ;\) (e) \(\mathrm{CN}^{-} ;\) (f) \(\mathrm{CN}^{+} ;\) (g) BN.

Short answer

The molecular orbital diagrams for these molecules and ions involve determining the total number of electons and filling in the orbitals from lowest to highest energy. For \(\mathrm{NO}\), there are 11 electons, one in \(\sigma_\mathrm{2s}\), one in \(\sigma^*_\mathrm{2s}\), two in \(\sigma_\mathrm{2p}\), four in \(\pi_\mathrm{2p}\), one in \(\pi^*_\mathrm{2p}\), and none in \(\sigma^*_\mathrm{2p}\). Follow this procedure for the other molecules and ions.

Step-by-step solution

Electron Configuration

First determine the total number of valence electrons in the molecule or ion. Use the electron configuration of each atom to determine this. For example, if we consider \(\mathrm{NO}\), Nitrogen (N) has 5 valence electrons and Oxygen (O) has 6, giving us a total of 11 electrons.

Construct the Diagram

Draw a horizontal line to represent each molecular orbital. The energy levels of the atomic orbitals of nitrogen and oxygen are similar, so we can place them at the same energy level. The general order for energies of molecular orbitals is \(\sigma_\mathrm{2s}, \sigma^*_\mathrm{2s}, \sigma_\mathrm{2p}, \pi_\mathrm{2p}, \pi^*_\mathrm{2p}, \sigma^*_\mathrm{2p}\). Fill the molecular orbitals with the 11 electrons, starting from the lowest energy orbital and going upwards. If an orbital is filled, proceed to the next one. The π_\mathrm{2p} orbitals can hold 4 electrons, so fill both orbitals with two electrons each. The last electron will go into the \(\pi_\mathrm{2p}\) anti-bonding orbital.

Repeat the Process

Repeat steps 1 and 2 for \(\mathrm{NO^{+}}\), \(\mathrm{CO}\), \(\mathrm{CN}\), \(\mathrm{CN^{-}}\), \(\mathrm{CN^{+}}\) and \(\mathrm{BN}\). Remember that a positive charge means one less electron, a negative charge means an extra electron, and that Carbon (C) and Boron (B) both have 4 valence electrons

Key concepts

Heteronuclear Diatomic Molecules

Heteronuclear diatomic molecules consist of two different types of atoms tightly bonded together. For example, the molecules such as \(ox\), \(o^+\), and \(cn^-\) are all heteronuclear. It's important to distinguish these from homonuclear diatomic molecules, which contain two identical atoms, like \(n_2\).
These types of molecules are crucial because their different atoms bring the challenge of varying atomic sizes, electronegativities, and energy levels. This results in a more complex molecular structure.
The difference in these characteristics between the combining atoms affects the way their atomic orbitals interact to form molecular orbitals. In heteronuclear molecules, the molecular orbitals are not symmetrically distributed. This can often lead to polarity in the molecules, due to an unequal sharing of electrons.

Molecular Orbital Diagrams

Molecular orbital diagrams illustrate the energy levels of molecular orbitals within a molecule. These diagrams help us understand how atoms combine and share electrons to form a stable molecule.
Constructing a molecular orbital diagram involves drawing lines to represent different energy levels in a molecule. Each line corresponds to a specific molecular orbital, such as \(\sigma_{2s}\), \(\sigma^*_{2s}\), \(\pi_{2p}\), and so on.
The diagram starts with the atomic orbitals of the individual atoms and proceeds by showing how these orbitals overlap to form the molecular orbitals of the resulting molecule.
For heteronuclear diatomic molecules, the energy levels of these orbitals may differ due to differing atom size and electronegativity, often making one atom contribute more to bonding or anti-bonding orbitals. This can be illustrated quite effectively in diagrams by using the relative heights of the energy levels.

Valence Electrons

Valence electrons play a critical role in determining the chemical properties and reactivity of an atom. These are the electrons located in the outermost shell of an atom.
For creating molecular orbital diagrams, counting the total number of valence electrons is the first step. For instance, considering the molecule \(\mathrm{NO}\), Nitrogen provides 5 valence electrons and Oxygen contributes 6, leading to a total of 11 valence electrons for the entire molecule.
Understanding valence electrons helps us to determine the molecular structure. It tells us how electrons will be distributed across the molecular orbitals.

• In a neutral heteronuclear molecule, sum up the valence electrons of both atoms involved.
• For ions, adjust the total count by adding electrons for negative charges or subtracting them for positive charges.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom or molecule across various orbitals. When talking about molecules, it helps us figure out how electrons are arranged across molecular orbitals, influencing the molecule's stability and properties.
With a heteronuclear diatomic molecule, the electron configuration starts by calculating the number of electrons. For example, \(\mathrm{NO}\) has 11 valence electrons, which we distribute across different molecular orbitals.
To do this:

• Begin with filling the lowest energy molecular orbitals first, such as \(\sigma_{2s}\).
• Move to the next orbital only after the previous one is filled. Keep in mind that orbitals like \(\pi_{2p}\) can hold up to 4 electrons.
• Address anti-bonding orbitals (\